Investigation Of Hull Damage Due To Ship Collision Based On Peridynamic Differential Operator

Ship collision and grounding accidents are major hazards during ship operation,since they may result in severe financial loss,environmental damages and even loss of human lives.Therefore,the crashworthiness of ship has aroused greatly concerns in ship design and construction.The process of ship collision and grounding is always accompanied with drastic plasticity and fierce fracture,and it’s a great challenge to the simulate by finite element method(FEM).On the one hand,FEM is a kind of mesh-based method of which the accuracy mainly depends on the quality of mesh grid.Once the distortion of grid happens,which usually appears in the large deformation analysis,the calculation would be significantly affected and even ends up in collapse.On the other hand,since the completeness of mesh grid is required in traditional FEM,the crack path is not allowed to propagate through the mesh grid.On account of the limitations mentioned above,a novel meshfree particle method based on peridynamic differential operator(PDDO)is propose to overcome these difficulties.Without the mesh grid,this method is flexible to deal with large plastic deformation and crack propagation.Furthermore,peridynamic differential operator(PDDO)enables numerical differentiation through integration,which makes the evaluation of derivatives much easier in the presence of jump discontinuities or singularities.In this dissertation,the proposed meshfree particle method is employed to establish a numerical model for the simulation of ship collision and grounding.The purpose of this work is to predict the damage and evaluate the resistance capability of ship structure during the impact process,and to provide an effective numerical tool for the design of ship crashworthiness.The basic idea and setup procedure for PDDO is demonstrated first,and the formula of PDDO in 2D case is derived in detail.To validate its accuracy,three different types of functions in 2D case are adopted and their zeroth(the function itself)and first order partial derivatives could be given analytically.Then the PDDO is employed to recover these items numerically and the results are compared with analytical ones for the purpose of accuracy validation.Afterwards,PDDO is adopted to solve kinematic equation in 2D case and the numerical model for plane stress analysis is established.To verify the accuracy of the proposed model,the elastic deformation of a cantilever beam and a plate with hole is calculated.Based on Mindlin-Reissner plate theory,the previous model could be extend to 3D case.The displacement of a certain point in shell plate could be decomposed into the linear and angular parts according to Mindlin theory.Thus,two sets of governing equations,namely the conservation equation of linear momentum and angular momentum,are set up and its Galerkin weak form could be easily derived.Then by discretizing the kinematic values in governing equations through PDDO,the 3D shell model could be established.Finally,various numerical examples are conducted to verify the convergence and accuracy of proposed model.On account of drastic plastic deformation that happens in ship collision,it’s necessary to introduce the plasticity constitutive relation into previous shell model.The material nonlinearity is numerically demonstrated with Von Mises yield function and the constitutive relation is updated with return mapping algorithm.To verify the accuracy of proposed model,an ultimate strength experiment is carried out in this work.In the experiment,a stiffened plate with hole is adopted as specimen and sustains the axial compression during the test.The resistance force of specimen is recorded and used as comparison data to verify numerical model.After the simulation of test with proposed model,the results exhibits a good agreement with experiment and its applicability and accuracy proved.As for the ship collision problem,two main aspect should be taken into account.First,the accurate calculation of impact force is necessary.In this work,the impact surface is regarded as the stiffen surface and could be discretized into small surface element for the detection of penetration particle.Once the penetration is detected,the impact happens and the impact force is calculated according to the penetration distance of the particle.On the other hand,the simulation of material fracture during the impact is also important.In this work,the GursonTvergaard-Needleman(GTN)damage model is adopted to estimate the failure of material.Once the damage value exceeds the preset threshold,the fracture would happen.The particle split algorithm is proposed for establishment of crack surface during the simulation of crack initiation and propagation.The support domain of particles around new generated crack surface should be updated based on visibility condition.To verify the proposed methodology,an indentation test is conducted and used as the reference object to simulate.After comparison,the simulation result is in good agreement with the experimental data and it proves the accuracy of proposed methodology.For the purpose of verifying the practicability of proposed methodology in engineering applications,the numerical simulations of ship side collision and bottom grounding are conduct.The results are compared with those from FEM,and a good agreement is obtained.Consequently,the proposed methodology has been proved with satisfied accuracy and sufficient capability in simulation of ship collision and grounding problems.